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1 Immigration and Internal Mobility in Canada Appendices A and B by Michel Beine and Serge Coulombe This version: February 2016 Appendix A: Two-step Instrumentation strategy: Procedure and detailed results In this appendix, we detail the procedure and results of the instrumentation strategy used in Section to cope with the potential occurrence of unobservable province-specific shocks. If these unobservable shocks are correlated with the inflows of the TFWs, then the FGLS estimates of the structural model to be estimated (see equation 11) can be biased. The IV procedure basically requires us to use an instrument that is correlated with the observed inflows of TFWs but uncorrelated with the error term and hence with the unobservable shocks. We need to emphasize that these shocks and the instrument are time- and province-specific. Our IV procedure builds on the previous strategies implemented in the literature of growth, trade, and migration. See Frankel and Romer (1999) for an application to the impact of trade on growth. It has also been used in the literature on international migration (see Spilimbergo [2009]; Beine, Docquier, and Schiff [2013], among others). The present strategy extends the previous contributions in the sense that we use a panel dimension while the previous papers dealt only with cross-sectional data. The procedure involves two main separate steps. For the sake of clarity, the first step can be broken down further into separate substeps. A.1.1 First step: Gravity model and aggregate predicted inflows of TFWs by province In this first step, we use a gravity model applied to the bilateral flows of TFWs between each country of origin of the world and each province in each year. The model is used to generate predicted bilateral flows for each triplet (origin country destination province time) that are afterwards aggregated across countries of origin to generate our instrument. This instrument is the time-varying, province-specific aggregate predicted inflows of TFWs. The prediction is supposed to be generated by exogenous factors, i.e., covariates of the gravity model that are uncorrelated with the unobservable shocks (and the error term) of equation (11). We first estimate the following benchmark gravity model: ln (1 + m ij,t ) = α i + α j + α t + β 1 ln (d ij ) + β 2 l ij + β 3 M ij,t 1+ γ f(y it ) + ε ij,t (A1). The gravity model involves a log-log specification explaining the log of the number of TFWs m ij,t each year t between country of origin i and province j. This specification can be more or less justified on the basis of microfoundations with optimizing agents (see Beine, Bertoli, and Fernandez-Huerta-Moraga [2014] for a survey). Since there are many pairs with zero bilateral flows or even missing bilateral flows, the use of ln (m ij,t ) would generate estimations that are subject to a significant selection bias. We can indeed expect that countries that do 1

2 not send any TFWs to a given province do not share the same observed and unobserved features as those of the countries sending TFWs. The same line of reasoning can apply to missing data about the flows. To avoid that, we use the usual trick of taking ln (1 + m ij,t ) (the so-called scaled estimation procedure) to include the zeroes in the estimation. Further to that, we also have to deal with the missing data. Looking at the database (kindly provided by Citizenship and Immigration Canada [CIC]), we notice that most of the missing data was found for triplets for which zero flows were observed during other years. If this is correct, we can transform the missing data into zeroes, which would involve even more observations. We follow both procedures and check that the results are qualitatively and quantitatively similar. Model (A1) involves either covariates or fixed effects. With respect to fixed effects, we include country of origin fixed effects α i that capture the time-invariant characteristics of origin countries such as geographical location. We also include the destination province fixed effects α j that capture the time-invariant characteristics of receiving provinces such as geographical location or language. Finally, we include time fixed effects that capture the general factors affecting the migration of TFWs. These include important factors such as the Canada-wide immigration policy regarding these TFWs. We use two time-invariant factors affecting the relative attraction between each country of origin and each province. First, we use geographic distance d ij between each origin country and each province, using the respective capitals as references. Second, we use linguistic proximity measures denoted by l ij. Note that Canada is mainly an English-speaking country with the exceptions of Quebec, which is French-speaking, and New Brunswick in which both languages are spoken. l ij is broken down further into two variables, one for French, one for English. The two variables are dummy ones taking 1 if the origin and the destination share the same language, 0 otherwise. The l ij and d ij variables are exogenous with respect to unobserved shocks. We also capture in model (A1) some network effect regarding the TFWs. The migration of workers has been shown to depend a lot on migrants networks at the macroeconomic level (see Beine, Bertoli, and Fernandez- Huerta-Moraga [2014]). These networks are related to the stock of previous migrants in the destination province who came from the same origin. For TFWs, however, this concept is not directly applicable since these are temporary migrants who have to return to their country at the end of the year. Still, some network effect definitely exists in the process of hiring TFWs. In hiring TFWs from a specific origin, Canadian employers obtain some information about productivity, efficiency, and so on of that origin s workers from previously hired TFWs from the origin. But these important revelations can be asymmetric. Furthermore, if employers are satisfied with the previous TFWs, employers can hire the same workers provided they return to their origin and reapply to the program. Anecdotal evidence of farmers in Quebec repeatedly hiring agricultural workers from Honduras as TFWs is a good illustration of that phenomenon. We capture this particular network effect by summing up the flows of previous TFWs over the last five years. This variable is denoted by M ij,t 1. If unobserved shocks to the province are not too persistent over time, this variable is also exogenous with respect to unobserved shocks. 2

3 Finally, we include origin-specific income shocks y it. We use GDP per head data from the Penn World Tables (version 8.0)1 in several functional forms. In a first one, we simply use the log of GDP per head, i.e., γ f(y it ) = β 4 ln (y it ). This could capture the role of the wage differential between the origin and Canada, and we should expect a negative coefficient if this mechanism is prevailing. Nevertheless, the literature on migration shows that income at origin can have a non-linear effect. See Mayda (2010 and Beine, Bertoli, and Fernandez-Huerta- Moraga (2014) on that. Low income levels can be associated with little emigration because liquidity constraints are operating. As income increases, this releases these constraints and leads to more migration. After some threshold, when constraints are no longer operating, further increases lead to a reduction in the wage differential and therefore deter emigration. In that case, one should expect a concave relationship. In this functional form, we have γ f(y it ) = β 4 y it + β 5 y 2 it. Income shocks at origin y it are obviously uncorrelated with province-specific shocks and can be therefore considered as exogenous factors. Table A1 presents the results of the estimation of equation (A1) with different variants. The results of the gravity regressions are more or less in line with the expectations. Flows of TFWs to a given province from a given origin increase with linguistic similarity, decrease with distance, increase with the size of the previous flows of the TFWs. The role of origin-specific GDP shocks receives less support from the data. While the signs of the coefficients are consistent with the expectations, they are mostly insignificant. This might due to the fact that what matters for migration decisions is the wage at origin. GDP per head might be a poor proxy for the wages in a lot of cases. This issue has already been identified in the existing literature on gravity models applied to international migration (see Beine, Bertoli and Fernandez-Huerta-Moraga [2014[ among others). The different specifications (1) to (6) give fairly similar results. The R2 vary between 0.83 and 0.90, which suggests that the prediction should be quite good, at least at the bilateral level. The fact that missing data are transformed into zero values leads to a slightly less-good fit; this is understandable since, in some cases, this might be too strong an assumption. One should be aware that each model will give rise to a different instrument, so a choice has to be made for the subsequent instrumentation procedure. In Section 4.3.2, we use the instrument generated by model (6). Nevertheless, the results of the final IV estimation do not depend in general on that choice since the results are qualitatively and quantitatively similar across the six possible instruments. 2 A.1.2 Prediction of bilateral flows of TFWs 1 Actually, the database of bilateral flows to each province transmitted by CIC includes up to 251 origins (the maximum number is for Ontario). While most of these origins are countries, a subset includes regions of some countries. (The remaining origins are aggregates of countries like East Africa and are omitted.) A good example is provided by the four overseas departments of France (Guyana, Guadeloupe, Martinique, and La Réunion) for which the flows are distinct from the ones coming from Metropolitan France. Aggregating the flows with those coming from Metropolitan France would include some bias since these departments differ significantly from the Metropole, especially in terms of distance to Canada but also in terms of income levels. It is still interesting to include these regions since they send many migrants to Canada and especially to French-speaking Quebec. For these entities, we calculated our own GDP per head data since they are not available in the Penn World Tables (version 8.0). We use data of Insee (Institut National de la Statistique et des Études Économiques) for 2009, 2010, and For the rest of the sample period, we applied the ratio department/metropole to the French data to get GDP per head estimates of these origins. 2 All the results are available upon request from Michel Beine. 3

4 Once model (A1) has been estimated, one can recover the estimates of the fixed effects and the coefficients to predict each bilateral flow of TFWs between each origin and each province of destination at each point of time. Let us denote by α the vector of the estimated fixed effects, and denote θ as the vector containing the estimated slope coefficients (β, 1 β, 2 β, 3 β, 4 β ) 5 from model (A1). Finally, let us collapse in vector X ijt the covariates used in each regression. Then we have: (1 + m ij,t ) = exp (α + θ X ijt ). (A2) A.1.3 Prediction of inflows of TFWs by province and by year We then can use the predicted m ij,t at the dyadic level to produce a predicted aggregate value for each province at each point of time. This is obtained simply by summing up across origins for each province in each year: m j,t N = i=1 m ij,t. (A3) The predicted m j,t can be used subsequently as an instrument for the observed values of TFWs by province and time period. The validity of these instruments has to fulfil the usual two conditions. First, the instruments must be strong predictors of the observed TFWs. The estimates of Table A1, in particular the values of the R2, suggest that this is the case at the bilateral level. Furthermore, at the aggregate level, i.e., after summing up across origins, this can be evaluated by the F-stat of the first stage of the final IV procedure. The values of the F-stats reported in Table 5 in the core of the text are far beyond the usual threshold of 10. The second condition is that the instrument must be uncorrelated with the error term of the final regression. In this case, the error term contains the influence of unobserved provincial shocks on the net interprovincial immigration flows of native workers. The covariates used for the prediction of m j,t and m j,t are obviously uncorrelated with the contemporaneous shocks. The exclusion restriction can be questioned only for our measure of the network effect M ij,t 1 if these shocks are highly persistent over time. Nevertheless, instruments generated without the inclusion of M ij,t 1 give qualitatively similar results.3 3 Once again, these results are available upon request from Michel Beine. 4

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